Such apparatus is known for a motorized two-wheeled vehicle of the type having a water-cooled internal combustion engine mounted thereon in which a radiator for cooling the engine is mounted between left and right tubular frame elements of the vehicle body. This conventional arrangement, however, is deficient in that not only will air flow produced by vehicle travel not be fully directed to the radiator because of the existence of the front wheel, front fork and other members in front of the radiator, but also, because the air flow supplied to the radiator is turbulent, the radiator itself serves as a resistance thereto and the air flow is forced to flow right and left whereby the rate of air flow to the radiator becomes insufficient, and thus the cooling efficiency thereof is lowered.